Rate control means for target trackers



Dec. M, i951 2,578,202

1K. B. PALME RATE CONTROL MEANS FOR TARGET TBACKERS Filed Feb. 2e, 1947 justed by the observer. ,mine the angular velocity of the telescopic sight Patented Dec. l1, 1951 RATE CONTROL MEANS FOR TARGET TRACKERS Karl Bertil Palme, Bofors, Sweden, assignor to Aktiebolaget Bofors, Bofors, Sweden, a corporation of Sweden Application February 26, 1947, Serial No. 731,114

Swedenv April 28, 1941 Claims. (Cl. 235-6L5) This invention relatesto rate control means for tracking of moving targets, such as aeroplanes. The speed of a projectile aimedat an aeroplane is not infinite in comparison to that of the plane, and hence in shelling airplanes with anti-aircraft artillery, the point at which projectile and plane will meet must be calculated from the point at which the plane is seen at the moment of firing, along the course of the plane.

As changes in direction or speed of the plane can seldom be foreseen, it is generally assumed that the plane during the travel time of the projectile continues its course along the tangent of the trajectory in the observed or present position of the target. Uninterrupted observation of the target position and familiarity with the ballistic properties of the gun permit determination of the meeting point and therewith the angle of direction of the gun and the fuse setting time (factors relating to artillery fire). The observations for this purpose consist of measuring the angle of azimuth, the angle of elevation and the distance of the target. Although continuous goniometry can be undertaken with great accuracy, available rangenders result in an error of about 1% for 6000 meter distance-if the personnel is trained. In times of war and for less experienced personnel, a multiplication of the error has to be expected. The most modern procedure for rangelnding consists of maintaining the correct distance, so that the results may be considered as approximately continuous. Nevertheless, a continuous distance measurement with accidentally distributed errors not only results in a faulty range value. but worse still, causes constant changes in the direction of the tangent of the trajectory which changes do not at all correspond to actuality.

AFor older fire control instruments the pursuit of the target was so performed, that the telescopic sights and preferably the whole instrument, were manually rotated by the azimuth observer in the horizontal or azimuth plane and correspondingly upward by the quadrant sight observer. (Coincidence of coordinates.)

' For newer fire-arms, the rotation of the telescopic sight is done automatically by friction gears with variable gear-ratios which are ad- The gear-ratios deterand constitute a measure for these velocities. The observers have to watch that the angular velocities coincide with those of the target, once coincidence of the coordinates has been brought about. (Coincidence of derivatives.) These tracking-methods are convenient, as long as the angular velocities change slowly.

One of the objects of this invention is to provide a novel and improved rate control means for automatic target tracking apparatus for tracking targets moving through space in which the coordinates of the target are measured continuously in a given co-ordinate system, for example spherical coordinates consisting of the angles of elevation and azimuth and the range of the target are continuously measured.

According to a now preferred embodiment of the invention the aforementioned object of the invention and other objects which will be pointed out hereinafter are attained by providing in an automatic target tracking apparatus for tracking targets moving through space, means representing the lthree coordinates y and z of a point P in a rectangular coordinate system and comprising three rotatable shafts; drive means for continuously and automatically rotating the said shafts, said drive means comprising a shaft for the rate of change of a shaft for the rate of change y of y and a shaft for the rate of change z' of z; control means comprising a iirst rotatable actuating element for changing the rate of change a' of the azimuth angle a, a second rotatable actuating element for changing the rate of change of the elevation angle and a third rotatable actuating element for changing the rate of change L' of the range L of the point P; and transmission means operatively connecting said actuating elements with said shafts of the drive means, the said transmitting means being arranged to transmit a rotation of the rst element through an adjustment angle Aa at the rate -sine a of said angle Aa' to the shaft for ar' and a rotation of the said element at the ratio cos a of said angle Aa' to the shaft for y', and a said angle A to the shaft for x' and a rotationof the second element at the rate sine sine a of said angle Ap to the shaft for y', and a rotation of the second element at the rate cos of said angle A' to the shaft for z', and a rotation of the third element for altering the rate of change L' through an adjustment angle AL' at the rate cos a. cos p of said angle AL to the shaft for 1:', a rotation of the second element at the rate cos sine a of said angle AL to the shaft for y', and a rotation of the third element at the rate sine of said angle AL to the shaft for e'.

Such an arrangement according to the invention results in a practically completely auto-l matic target tracking operation of the apparatus. Once correctly set, the apparatus changes automatically and continuously its angular velocities in correspondence with those of the target. It also changes continuously its range indications in correspondence with the actual target distance, and this as long as the target pursues its course with unchanged speed along the tangent of the trajectory in the observed or present position of the target.

The arrangement can for example be constructed so that the point determined by the coordinates y and e can then-through manual adjustments of the corresponding speed changes 1:', y' and a'-receive a uniform motion (with regard to magnitude and direction), although otherwise arbitrary and selectable. If these speeds are selected correctly so that they correspond to the actual speeds of the target in space, the point m, y, a, will always correspond to the actual position of the target in space. The automatic tracking results through the following: the apparatus computes continually from the momentary coordinates y, and a the corresponding angles of azimuth, and elevation, and the target distance. Furthermore, the apparatus places the telescopic sight in agreement with these angles, and the adjustment element of the rangender in agreement with the distance of the target.

With such an apparatus, the observers for the angles of elevation and azimuth, and the range do not have to make any readjustments, once the instrument has been properly set, and as long as the speed vector of the target does not change.

In case the apparatus tends not to follow the target properly, it becomes apparent that the value set for one or several of the values y' and z' is no longer correct and needs readjustment. As target observation is carried out in spherical coordinates, one or several of the observers will realize that the tracking is too fast or too slow. They cannot, however, decide which of the values r', y and a' should be changed. The great di'iculty which this circumstance would normally entail is completely eliminated through the novel arrangement of the elements, by which the manual adjustment of the second instrument is brought about. For each magnitude observed, an adjustment element is provided. Each of these elements controls, in case of its readjustment, the variable speeds of as', y' and a of the coordinates of the rectangular coordinate system at such a ratio, that in the first mentioned spherical coordinate system of the apparatus an immediate change of the variable speed of the readjusted element only occurs, while the variable speeds of the other observed magnitudes do not undergo any change. If, for example, at a given moment, the observer of the azimuth notes, that the tracking is too slow, he cannot decide at which ratio the magnitudes of the three units y' and e' should be changed in order to correct the setting of the angle of deviation without also changing the presumably correct setting of the angle of elevation and the setting of range. The arrangement according to the invention causes automatically, that, depending upon each momentary value of as', y' and e', the corrective change as brought about is distributed at the proper ratio over the three variables.

The target tracking in general precedes the so-called trapping of the target. For this too,

it is important, that the three observers can Work simultaneously, without disturbing one another in their work. This important objective too, is fully attained through the arrangement according to the invention.

The above mentioned, as well as other objects of the invention are more fully explained hereinafter in connection with drawing. To facilitate the understanding of the invention, it is assumed that the rate control means employ a rectangular coordinate system. However, the invention is also applicable in case a system of coordinates, other than a rectangular one is used. The rate control means must then, of course, be designed according to the requirements of the employed coordinate system.

Other and further objects, features and advantages of the invention will appear hereinafter and in the appended claims forming part of the application.

In the accompanying drawing a now preferred embodiment of the invention is shown by way of illustration and not by way of limitation.

In the drawings:

Fig. 1 is a diagram showing the relationship between the three coordinates x, y and a and the lobserved polar values for the azimuth, quadrant sight and range; and

Fig. 2 shows diagrammatically rate control means according to the invention.

Referring now to Fig. 1 in detail, this gure shows a conventional rectangular coordinate system in which the target is designated by P. This point can be dened in two Ways, to Wit, by its position in space in relation to each of the three coordinate-axes (designated y, e) or by means of the observed values, namely the azimuth a, in this case the angle between the .fr-axis, and the projection of the connecting line between the point and the zero-point on the x-y plane, further the quadrant angle in this case the angle between the connecting line mentioned and the projection, and finally the distance L between the zero-point and the said point. Hence, the following relationship is the direct result for these three values:

=L cos cos a y=L cos sin a 1 z=L sin Upon differentiation of 1) d=dL cos cos a-dL sin cos a-daL cos sin a dy=dL cos sin a dL sin sin a-l-daL cos cos a dz=dL sin -l-dL cos 2 It shall now be investigated, what might have occurred, if at the point of observation one error only for one of the three values observed were discovered.

If one error is observed in L; then:

dLeO da=0 3 d=0 According to Equation 2, these conditions are fullled only if:

d=,u cos cos a dgl/:fl cos sin a 4 da=jl sin If on the other hand an verror kis observed in the azimuth a only, thev following is true:

This condition is fulfilled according to (2) if the following is true:

drr=pL cos sin a (1g/:ML cos cos a 6 If finally an error is observed in the quadrant sight only, the following condition is valid:

dL=0 da=0 7 deo These conditions are satisfied by Equation 2, provided that:

In the above mentioned equations, p. represents a small factor which represents a possibly occurring error.

If nally rc, y, and z in Equation 1 are derivated with respect to time, one obtains:

x'=L' cos cos a-L sin cos a-a'L cos sin a 'y'=L cos sin a-L sin sin a-I-a'L cos cos a 9 z'=L' sin -I-L cos A differentiation of Equation 9 results in: d:z:=dL cos cos a-d'L sin cos a-da'L eos sin a dy'=dL' cos sin a-dL sin sin a-I-da'L cos ,8 cos a de'=dL' sin -i-d'L cos It shall now be examined under what conditions the above mentioned conditions according to Equations 3, 5, and 7 are fulfilled.

It appears that conditions 3 are fullled if,

dy=;w' cos sin a 11 d2'=/.L' Sin To fulll conditions 5, it is necessary that cZ'=-a' cos sin a dyL- p' cos cos a 12 a small factor, which represents the corrections,

obtained upon a small change of y, and z respectively.

Comparing Equations 4, 6 and 8 with Equations 11, 12, and 13, it is apparent that the presented problem is solved, when an apparent change of L' only results by distribution of increments m', y' and z', if any, according to Equation 4. Also, when an apparent change of azimuth angle a only results, if one distributes increments to .'v, y and e according to Equation 6. An apparent change of the angle of elevation only results if increments to zr', y and e are distributed according to Equation 8.

Fig. 2 shows a diagrammatic embodiment of a rate control means for mechanically attaining these results.

The rate control means according to Fig. 2 comprises three disc I4, I5, I6 rotated continuously at constant speed. These discs engage frictionally rollers I1, I8, I9 respectively. Rollers I1,

I8 and I9 are operatively connected with three threaded shafts 26, 2l and 22 respectively, on which nuts 23, 24, and 25, respectively are threaded. These nuts, finally, are connected with one or several elements of the fire control instrument, which elements serve to indicate the values of y, and z.

Friction rollers I1, I8, I9 are slidably mounted on their respective shafts, so that by means of claw-like elements 26, 21 and 2B respectively, they can be shifted to a position of smaller or larger radius in relation to the center of the friction discs I4, I5 and I6, thereby varying the transmission ratio. It will now be apparent that this transmission ratio, or in other Words, the radial position of the friction rollers I1, I8 and I9 relative to the center of the friction discs I4, I5 and I6 indicates the value of the units which were designated with x', y and e' in the previously stated equations. These values shall be controlled in accordance with Equations 11, 12 and 13. For this purpose the following arrangement has been made:

Each of the hand-wheels for the observers of the angles of elevation, azimuth and range, designated by 29, 39, and 3l in Fig. 2, supports a screw which -coact with threaded friction discs 32, 33 and 34 respectively so that these friction-discs are rotated when the respective hand wheels 29, 39 and 3| are rotated. Disc 32 is in frictional engagement with two rollers 35 and 36. Each one of these rollers is slidable on its axle 39, 44 respectively by means of two claw-like elements 31 and 38. These elements 31 and 38 are driven from the apparatus in such a way, that element 31 maintains roller 35 continuously at a distance from the center of friction disc 32 proportional to cos while claw-like element 38 maintains roller 36 continuously at a distance proportional to sin Axle 39 of friction roller 35 is connected with a threaded shaft 42 by a bevel gear 40 and a differential gearing 4I, the purpose of which will be explained hereinafter. Shaft 42 displaces a nut 43 threaded thereupon and connected with claw element 28. Axle 44 of friction-roller 3,6 rotates a friction disc 46 through an axle 41 and a differential gearing 45. Disc 46 is frictionally engaged by two radially displaceable frictionrollers 48 and 49. The claw-like elements for displacement of these rollers are designated by 50 and 5I. Element 50 is connected with the apparatus in such a way, that the distance of roller 48 from the center of disc 46 is maintained proportional to cos a. Element 5I for the displacement of roller 49 is connected with the apparatus in such a way, that this roller is displaced proportional to sin a. The axle 52 of roller 48 is connected by a bevel-gearing 53 and a differential gearing 54 with a threaded shaft 55, which displaces element 26 through a nut 56 threaded upon shaft 55. The axle 51 of roller 49 is connected by a planet gearing 58 with a threaded shaft 59, which displaces element 21 through a nut66.

Disc 33 is similarly engaged by two friction rollers 6I and 62, whose displacing elements 63 and 64 are controlled by the apparatus in such a way, that roller 6I is displaced proportional to -sin a and roller 62 proportional to cos a. Axle 65 of roller 6I is connected by a bevel gearing 66 with differential gearing 54 and axle 61 of the roller 62 with differential gearing 58.

Finally, disc 34 is engaged by two friction rollers 68 and 69, whose displacing elements 10 and 1I cause the displacement of the rollers to be proportional to sin and cos respectively. Axle 12 of roller 68 is connected by a bevel gearing 13 with differential gearing 4|, While axle 14 of roller 69 is connected with differential gearing 45 by a bevel gearing 15.

In order to explain the operation of the system, let it be first assumed, that the observer of the angle of elevation and the angle of deviation nd satisfactory adjustment, while the range observer notices a range-error, the target being at a greater or smaller distance than the one indicated by lthe apparatus. He then operates his handwheel 3| in such a way, that the range-error is decreased. This operation is transmitted to all the elements 26, 21 and 28, although at different ratios as will be seen from the following.

The movement of hand Wheel 3| is transmitted to axle 14, gearing 15, differential gearing 45, axle 41 and friction disc 46, at the ratio of cos From friction disc 46 it is transmitted to axle 52, gearing 53, planet gearing 54 and threaded shaft 55 at the ratio cos a, with the result, that the speed of the rollers I 1 changes by an amount cos cos a of the movement of handwheel 3|. It is obvious, that this corresponds to Equation 11. The movement of the disc 46 is transmitted to axle 51 at a ratio of sin a as Well as by diierential gearing 58 to threaded shaft 59. As a result, the transmission ratio determining the value y by means of friction roller I8 is changed at the ratio cos sin a. This too agrees with the Equation 11. Finally, the movement of handwheel 3| is transmitted to axle 12, gearing 13, differential gearing 4| and friction roller I9 (which determines the value 2'), at a ratio sin all of this corresponding to the Equation 1l.

If the range observer and the quadrant sight observer nd the adjustment correct, while the observer of the azimuth believes a correction to be necessary, he turns hand wheel 319. The displacement of Wheel 3|!y is transmitted to roller IT at the ratio of sin a through axle 65, bevel gears 66, differential gearing 54 and threaded shaft 55. Displacement of wheel 39 is further transmitted to roller I8 at a ratio cos a, by axle 61, differential gearing 58 and threaded shaft 59. To roller I9 however, the wheel movement is not transmitted at all. A comparison with Equation 12, shows that this is correct, except for the factor cos This however, does not cause an error, as it is obvious, that the last component of the Equation 12 can be Written Thus, cos can be considered a constant factor, as the assumption was, that the observer of the angle of elevation did not nd cause to question the correctness of the indication of the quadrant sight. Of course, the factor cos varies with each quadrant of sight taken. The result is, that for one value of the quadrant of sight a larger turn of the handwheel 30 may prove necessary and for another value of the same a smaller turn of the wheel may be needed to correct one and the same error. This is the only influence, which the disregard of the factor cos causes. Naturally, a correction for this factor can easily be introduced, just as it has been done for other trigonometric factors affecting the device according to Fig. 2.

If nallv the range observer and the azimuth observer find good adjustment, but the quadrant sight observer needs to readiust, the latter turns wheel 29. The motion is transmitted at the ratio sin to axle 44, diiferential gearing 45, axle 41 and friction disc 46, as well as from disc 46 at a ratio cos a to roller I1 by axle 52, gearing 53, differential gearing 54 and threaded shaft 55. Roller I1 determines the value of 3:. Further, the motion of wheel 29 is transmitted at a ratio sin a from disc 46 by axle 51, differential gearing 58 and threaded shaft 59 to roller I8, which accordingly experiences a motion at the ratio of sin sin a. Finally, the motion of wheel 29 is transmitted by axle 39, gearing 4U, differential gearing 4| and threaded shaft 42 at the ratio cos to roller I9. A comparison with the Equation 13 indicates, that this too is correct.

As will appear from Equations 11, 12, 13, the manual turns of handwheels 29, 30 and 3| do not disturb one another. According to generally correct rules of superimposition it is apparent, that any kind of disturbance does not appear, even if two of the operators acccidentally move their handwheels at the same time.

The actuation of the handwheels for purpose of target trapping, as mentioned above, may cause a rather time-consuming job, until the tracking is clear. It happens quite easily, that the operator, in the intention to trap the target faster, moves the roller I1, I8 and I9 so much, that a much larger derivation of m, y and z is caused than the one to which the true movement of the target in space corresponds. The re-establishment of the speed without over-regulation often ensues substantial difficulties. In order to facilitate the trapping of the target, a connection between each of the three rollers I1, I8, and I9 on one hand and threaded shafts 20, 2|, and 22 on the other hand by diierential gearing 16, 11 and 18 respectively is provided. The third axles 19, 8U and 8| respectively of the latter are connected with special handwheels for the target trapping. By means of these wheels, which must not be moved while tracking the target, one can quickly adjust the Various measuring instruments to the target and then pursue the latter by means of handwheels 29, 30 and 3|.

It should be understood that the invention is useful not only in connection with apparatus for tracking for targets moving in space, but also for targets which are moving in a horizontal plane, as is the case for instance with motorized artillery. The number of variables is naturally reduced for such application.

While the invention has been described in detail with respect to a certain now preferred example and embodiment of the invention it will be understood by those skilled in the art after understanding the invention, that various change and modifications may be made without departing from the spirit and scope of the invention and it is intended therefore, to cover all such changes and modifications in the appended claims.

What is claimed as new and desired to be secured by Letters Patent is:

1. In an automatic target tracking apparatus for tracking targets moving through space, in combination means representing the three coordinates y and z of a point P in a rectangular coordinate system and comprising three rotatable shafts 29, 2|, 22; drive means I4, I1, I5, I8, I6, I9 for continuously and automatically rotating the said shafts, said drive means comprising a shaft 55 for the rate of change of a shaft 59 for the rate of change y of y and a shaft 42 for the rate of change a of a; control means comprising a first rotatable actuating element 30 for changing the rate of change a' of the azimuth angle a, a

attacca Second rotatable actuating element 21 for changing the rate of change of the elevation angle and a third rotatable actuating element 3| for changing the rate of change L' of the range L of the point P; and transmission means operatively connecting said actuating elements with said shafts 42, 55, 59 of the drive means, the said transmitting means being arranged to transmit a rotation of the rst element 30 through an adjustment angle Aa at the rate -sine a of said angle Aa' to the shaft 55 for :11' (through 33, 6|, 65, 66, 54 to 55) and a rotation of the said element at the ratio cos a of said angle Aa' to the shaft 59 for y (through 33, 62, 461, 58 to 59), and a rotation of the second element 29 through an adjustment angle at the rate sine cos a of said angle A' to the shaft 55 for :c (through 32, 36, 44, 45, 41, 46, 48, 52, 53, 54 to 55) and a rotation of the second element 29 at the rate -sine sin a of said angle A to the shaft 59 for y' (through 32, 36, 44, 45, 41, 46, 49, 51, 58 to 59), and a rotation of the second element 29 at the rate cos of said angle A' to the shaft 42 for z' (through 32, 35, 39, 40, 4| to 42), and a rotation of the third element 3| for altering the rate of change L' through an adjustment angle AL at the rate cos a cos of said angle AL to the shaft 55 for zc (through 34, 69, 14, 15, 45, 41, 46, 48, 52, 53, 54 to 55), a rotation of the second element 3| at the rate cos sine a of said angle AL to the shaft 59 for y (through 34, 69, 14, 15, 45, 41, 46, 49, 51, 58 to 59) and a rotation of the third element 3| at the rate sine of said angle AL to the shaft 42 for e' (through 34, 68, 12, 13, 4| to 42) 2. An apparatus as described in claim l, in combination with a plurality of disk-shaped elements 33, 32, 34, each rotatable by an element of said second group of control means 30, 29, 3|, a plurality of pairs of rotatable elements 6|, 62; 36, 35; 68, 69, the two elements of each pair rotated by one of said disk-shaped elements, the element of the first control means which corresponds to a maintaining a radial distance between the center of the disk-shaped element 33 coacting with the element 39 of the second control means eifecting altering a' and the two rotatable elements 6|, 62 coacting with the last mentioned disk-shaped element which radial distance for one (6|) of said two rotatable elements is proportional to sin a and for the other (62) rotatable element is proportional to cos a, while the element of the first control means corresponding to maintains for each of the diskshaped elements 32, 34 coacting with said elements 29, 3| for altering and L' of the second control means a radial distance between the center of said last mentioned disk-shaped element 32, 34 and said two coacting rotatable elements 36, 35; 68, 69, which radial distance for one (36; 68) of said last mentioned rotatable elements is proportional to sin and for the other (35; 69) rotatable element is proportional to cos 3. An apparatus as described in claim 1, in combination with a plurality of disk-shaped elements 33, 32, 34, each of the elements of said second group of control means 30, 29, 3| rotating one of said disk-shaped elements 33, 32, 34, a plurality of pairs of rotatable elements 6|, 62; 36, 35; 68, 69, the two elements of each pair rotatable by one of said disk-shaped elements 33, 32, 34, the element of the rst control means which corresponds to a maintaining a radial distance between the center of the disk-shaped element 33 coacting with the element 30 for altering a' of the second control means and the two rotatable elements 6 62, contacting with the last mentioned disk-shaped element 33 which radial distance for one (6|) of said two rotatable elements is proportional to sin a and for the other (62) rotatable element is proportional to cos a, while the element of the second control means which corresponds to maintains a distance between the centers of the disk-shaped elements 32, 34 coacting with the elements 29, 3| for altering vand L' of the second control means and the respective two coacting rotatable elements 36, 35; 68, 69 which radial distance for one (36; 68) of said last mentioned rotatable elements is proportional to sin and for the other rotatable element (35; I69) is proportional to cos a diiferential gearing 45 for adding the rotational movement of the rotatable element 69 having a center distance proportional to cos ,8 and coacting with the disk-shaped element 34 rotated by the element 3| for altering L of the second control means to the rotational movement of the rotatable element 36 having a center distance proportional to sin and coacting with the disk-shaped element 32 driven by said element 29 for altering of the second control means, an additional disk-shaped element 46 rotated by said differential gearing 45, and two elements 49, 48 coacting with said additional disk-shaped element 46 rotated by said diierential gearing 45, the element which corresponds to a of the first control means maintaining a radial distance between the center of said additional disk-shaped element 46 and said two rotatable elements 49, 48 coacting therewith which radial distance for one (49) of said lastmentioned two rotatable elements is proportional to sin a and for the other rotatable element (48) is proportional to cos a.

4. A target tracking apparatus as defined in claim 1, wherein said transmission means comprise a plurality of disc-shaped rotatable resolver elements 33, 32, 34 each operatively connected with the respective one of said actuating elements 30, 29, 3| for rotation thereby, a corresponding plurality of pairs of rotatable and axially displaceable members 6|, 62; 36. 35; 68, 69, the two members of each pair being in eccentric engagement with one of the faces of a respective resolver disc for rotation of the said members by said discs, and a plurality of ad justable control members 63, 64; 38, 31; 1|), 1|, each of the said control members engaging a respective one of said axially displaceable members so' as to vary the radial distance of the latter members relative to the rotational center of the resolver discs for varying the rotational velocity of the axially displaceable members, the said axially displaceable members being operatively connected with the respective ones of said shafts 55, 59, 42 for the rate of change x', y and e respectively, the positions of the adjustable control members 63, 64 engaging the axially displaceable members 6|, 62 rotated by the resolver disc 33 connected with the rst actuating element 36 being controlled by -sine a and cos a respectively, the positions of the adjustable control members 38, 31 engaging the axially displaceable members 36, 35 rotated by the resolver disc 32 connected with the second actuating element 29 being controlled by cos and sine respectively, and the positions of the adjustable control members 10, 1I engaging the axially displaceable members 68, 69 rotated by the resolver disc 34 connected with the third actuating element 3l being controlled by sine and cos respectively.

5. An apparatus defined in claim 4, in combination with differential gearing means 45 adding the rotational speed of the rotatable and axially displaceable member 69 controlled by cos and coacting with the third actuating element 3| .to the rotational speed of the rotatable and axially displaceable member 36 controlled by -sine and enacting with the second actuating element 29, an additional disc-shaped resolver element 46 rotated by the said diierential gearing means 45, two axially displaceable members 48, 49 in rotational and eccentric engagement with one of the faces of the said disc-shaped element for rotation of said members by the said disc 46 and two adjustable control members 50, 5| each engaging a respective one of the said two axially displaceable members 48, 49 so as to vary the radial distance of the latter members froml the center of the additional disc 46, the

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,065,303 Chafee et a1 Dec. 22, 1936 2,235,826 Chafee et al. Mar. 25, 1941 2,385,952 Svoboda Oct. 2, 1945 2,492,355 Campbell et al. Dec. 2'7, 1949 

